A DFOtechniquetocalibratequeueingmodels

A crucialstepinthemodelingofasystemistodeterminethevaluesoftheparameterstouseinthe model. Inthispaperweassumethatwehaveasetofmeasurementscollectedfromanoperationalsys- tem, andthatanappropriatemodelofthesystem(e.g.,basedonqueueingtheory)hasbeendeveloped. Not infrequentlypropervaluesforcertainparametersofthismodelmaybedifficulttoestimatefrom available data(becausethecorrespondingparametershaveunclearphysicalmeaningorbecausethey cannot bedirectlyobtainedfromavailablemeasurements,etc.).Hence,weneedatechniquetodetermine the missingparametervalues,i.e.,tocalibratethemodel. As analternativetounscalable“bruteforce”technique,weproposetoviewmodelcalibrationasanon- linear optimizationproblemwithconstraints.Theresultingmethodisconceptuallysimpleandeasyto implement. Ourcontributionistwofold.First,weproposeimproveddefinitionsofthe“objectivefunction” to quantifythe“distance”betweenperformanceindicesproducedbythemodelandthevaluesobtained from measurements.Second,wedevelopacustomizedderivative-freeoptimization(DFO)technique whose originalfeatureistheabilitytoallowtemporaryconstraintviolations.Thistechniqueallowsusto solve thisoptimizationproblemaccurately,therebyprovidingthe“right”parametervalues.Weillustrate our methodusingtwosimplereal-lifecasestudies.